Cyclic product theorems for polygons. II: Constructions using conic sections (Q5955143)

The author proves several theorems of the type: the cyclic products determined by certain points of intersection of the tangents in certain points to conic sections passing through five vertices of a given polygon are constant. Here cyclic products refer to the products of the signed ratios in which a set of points on the edges of a polygon divide those edges. These theorems can be seen as rather involved conics-analogues of the Menelaus and Ceva theorems. [For part I of the paper see the author, ibid. 24, No.~2-3, 551-571 (2000; Zbl 0959.51016)].